Download or read book Adaptations of the Conjugate Gradient Method to Optimal Control Problems with Terminal State Constraints written by John Kendall Willoughby and published by . This book was released on 1969 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of conjugate gradients (CG) has been shown to be a rapidly converging and efficient means of solving unconstrained optimal control problems. This dissertation presents some theoretical and computational characteristics of three modifications to the CG algorithm which make it applicable to control problems with terminal state variable constraints. The penalty function method and the projection method have been used to adapt ordinary gradient methods to constrained problems. It is concluded here that the penalty function technique is no more or less advantageous with the CG method than with other gradient techniques. The projection method is shown to be theoretically less compatible with the CG algorithm than with other gradient methods. However, a stepsize adjustment policy is suggested that preserves the rapid convergence that is characteristic of the CG method. It is also shown that nonlinear instead of linear terminal constraints cause no additional theoretical of computational difficulty. A third adaptation of the CG method is given which is original to this study. The method, called the modified conjugate gradient method (MCG), is applied to constrained problems by using constant Lagrange multipliers which converge to their optimal values as the iteration proceeds. A unique feature of the MCG method is that each control iterate produced by the method causes the constraints to be satisfied exactly. Furthermore, the technique is equally applicable to nonlinear and linear terminal state constraints. (Author).
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1979 with total page 990 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book A HUM Conjugate Gradient Algorithm for Constrained Nonlinear Optimal Control written by Ivan Borges Oliveira and published by . This book was released on 2002 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Cont.) Standard logarithmic barrier functions and Newton methods are employed to address the hard constraints on control variables of the type Umin
Download or read book Sequential Conjugate Gradient Restoration Algorithm for Optimal Control Problems Part 2 Examples written by J. C. Heideman and published by . This book was released on 1974 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: In another paper Heideman and Levy developed the sequential conjugate gradient-restoration algorithm for minimizing a functional subject to differential constraints and terminal constraints. In this report, several numerical examples are presented, some pertaining to a quadratic functional subject to linear constraints and some pertaining to a nonquadratic functional subject to nonlinear constraints. These examples demonstrate the feasibility as well as the rapid convergence characteristic of the sequential conjugate gradient-restoration algorithm.
Download or read book Sequential Conjugate Gradient Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints Part 2 Examples written by J. R. Cloutier and published by . This book was released on 1977 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first volume the sequential conjugate gradient-restoration alogorithm was developed for minimizing a functional subject to differential constraint, nondifferential constraints, and terminal constraints. In this report, sixteen numerical examples are presented, four pertaining to a quadratic functional subject to linear constraints and twelve pertaining to a nonquadratic functional subject to nonlinear constraints. These examples demonstrate the feasibility as well as the rapid convergence characteristics of the sequential conjugate gradient-restoration algorithm.
Download or read book Method of Conjugate Gradients for Optimal Control Problems with State Variable Constraint written by Thomas Shu Fong and published by . This book was released on 1968 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sequential Conjugate Gradient Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints Part 1 Theory written by J. R. Cloutier and published by . This book was released on 1977 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sequential conjugate gradient-restoration algorithm is developed in order to solve optimal control problems involving a functional subject to differential constraints, nondifferential constraints, and terminal constraints. The algorithm is composed of a sequence of cycles, each cycle consisting of two phases, a conjugate gradient phase and a restoration phase. The conjugate gradient phase involves a single iteration and is designed to decrease the value of the functional while satisfying the constraints to first order. The restoration phase involves one or more iterations and is designed to restore the constraints to a predetermined accuracy, while the norm of the variations of the variations of the control and the parameter is minimized, subject to the linearized constraints. The sequential conjugate gradient-restoration algorithm is characterized by two main properties. First, at the end of each cycle, the trajectory satisfies the constraints to a given accuracy. Second, the conjugate gradient stepsize and the restoration stepsize can be chosen so that the restoration phase preserves the descent property of the conjugate gradient phase.
Download or read book Method of Conjugate Gradients for Optimal Control Problems with State Variable Constraints written by T. S. Fong and published by . This book was released on 1978 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: A review of the computational method of conjugate gradients for linear and nonlinear operator equations is given with emphasis in applying this technique to state variable constraint control problems. The first and second Frechet derivatives of the performance functional are derived. The search directions generated in the iteration process for the optimal control are locally conjugate with respect to the second Frechet derivative. The convergence is along the expanding sequence of sets, the itersection of the linear spaces spanned by the search directions and the set of admissible controls. The computational technique is applied to two state variable constraint problems, in one of which a penalty function is employed to convert the constraint problem to an unconstrained one in addition to the approach considering the constraints directly. For this same problem the method of steepest descent also is studied, and comparison of the results obtained is made and discussed. (author).
Download or read book The Conjugate Gradient Method for Optimal Control Problems written by and published by . This book was released on 1967 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conjugate gradient method for the solution of optimal control problems governed by weakly singular Volterra integral equations with the use of the collocation method written by Henry Ekah-Kunde and published by GRIN Verlag. This book was released on 2017-07-28 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seminar paper from the year 2015 in the subject Mathematics - Applied Mathematics, grade: A, , language: English, abstract: In this research, a novel method to approximate the solution of optimal control problems governed by Volterra integral equations of weakly singular types is proposed. The method introduced here is the conjugate gradient method with a discretization of the problem based on the collocation approach on graded mesh points for non linear Volterra integral equations with singular kernels. Necessary and sufficient optimality conditions for optimal control problems are also discussed. Some examples are presented to demonstrate the efficiency of the method.
Download or read book Sequential Conjugate Gradient restoration Algorithm for Optimal Control Problems with Nondifferential Constraints and General Boundary Conditions written by A. K. Wu and published by . This book was released on 1978 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers the numerical solution of the problem of minimizing a functional subject to differential constraints, nondifferential constraints, and general boundary conditions. The approach taken is a sequence of two-phase cycles, composed of a conjugate gradient phase and a restoration phase. The conjugate gradient phase involves one iteration: the first variation of the functional is minimized, subject to the linearized constraints and a quadratic constraint imposed on the variations of the control, the parameter, and the missing components of the initial state. The restoration phase involves one or more iterations: in each iteration, the norm squared of the variations of the control, the parameter, and the missing components of the initial state is minimized, subject to the linearized constraints. Twelve numerical examples are presented in order to illustrate the performance of the algorithm. The numerical results show the feasibility as well as the convergence characteristics of the present algorithm.
Download or read book Conjugate Gradient Algorithms and Finite Element Methods written by M. Křížek and published by Springer Science & Business Media. This book was released on 2004-06-11 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: The position taken in this collection of pedagogically written essays is that conjugate gradient algorithms and finite element methods complement each other extremely well. Via their combinations practitioners have been able to solve complicated, direct and inverse, multidemensional problems modeled by ordinary or partial differential equations and inequalities, not necessarily linear, optimal control and optimal design being part of these problems. The aim of this book is to present both methods in the context of complicated problems modeled by linear and nonlinear partial differential equations, to provide an in-depth discussion on their implementation aspects. The authors show that conjugate gradient methods and finite element methods apply to the solution of real-life problems. They address graduate students as well as experts in scientific computing.
Download or read book Sequential Conjugate Gradient restoration Algorithm for Optimal Control Problems with Nondifferental Constraints Part 1 Theory written by and published by . This book was released on 1977 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sequential Conjugate Gradient Restoration Algorithm for Optimal Control Problems with General Boundary Conditions written by A. K. Wu and published by . This book was released on 1978 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers the numerical solution of the problem of minimizing a functional subject to differential constraints and general boundary conditions. The approach taken is a sequence of two-phase cycles, composed of a conjugate gradient phase and a restoration phase. The conjugate gradient phase involves one iteration and is designed to decrease the value of the functional, while the constraints are satisfied to first order. During this iteration, the first variation of the functional is minimized, subject to the linearized constraints and to a quadratic constraint imposed on the variations of the control, the parameter, and the missing components of the initial state. The restoration phase involves one or more iterations and is designed to force constraint satisfaction to a predetermined accuracy, while the norm squared of the variations of the control, the parameter, and the missing components of the initial state is minimized.
Download or read book Gradient Optimization and Nonlinear Control written by Lawrence Hasdorff and published by John Wiley & Sons. This book was released on 1976 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conjugate Gradient Type Methods for Ill Posed Problems written by Martin Hanke and published by CRC Press. This book was released on 2017-11-22 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations. The main tool for the analysis is the connection of conjugate gradient type methods to real orthogonal polynomials, and elementary properties of these polynomials. These prerequisites are provided in a first chapter. Applications to image reconstruction and inverse heat transfer problems are pointed out, and exemplarily numerical results are shown for these applications.
Download or read book Gradient Optimization Algorithms for Systems with Terminal Constraints written by Ronald B. Zmood and published by . This book was released on 1978 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application of optimization techniques to the derivation of predictive information for flight displays is being investigated in connection with operational situations involving large disturbances and manoeuvres. This note surveys current gradient methods for computing extremal solutions of optimal control problems for systems having boundary conditions but without state or control constraints. It is concluded that a two stage procedure is required, with the first stage using a first order gradient, while the second stage would use a higher order variable metric method. Proposals are advanced for further research on optimization algorithms. (Author).
